Use hook_leaflet_views_alter_points_data_alter to add category based icon to your markers shown with leaflet_views.

category_marker.php

<?php
/**
 * Implements hook_leaflet_views_alter_points_data_alter().
 */
function fewo_map_leaflet_views_alter_points_data_alter($result, &$points) {
 // Get node object of result.
 $wrapped_node = entity_metadata_wrapper('node', $result->nid);
 // Check if we have a category attached to node.
 $category = $wrapped_node->field_sight_category->value();
 if (!empty($category)) {
  // Check if we have a custom category icon for taxonomy term.
  $category_icon = $wrapped_node->field_sight_category->field_sight_icon->value();
  if (!empty($category_icon)) {
    // Create url for usage as marker icon.
    $icon_url = file_create_url($category_icon['uri']);
    // Set icon as marker icon for point.
    $points[0]['icon']['iconUrl'] = $icon_url;
  }
 }
}
?>